Density estimation in the uniform deconvolution model

We consider the problem of estimating a probability density function based on data that are corrupted by noise-from a uniform distribution. The (nonparametric) maximum likelihood estimator for the corresponding distribution function is well defined. For the density function this is not the case. We study two nonparametric estimators for this density. The first is a type of kernel density estimate based on the empirical distribution function of the observable data. The second is a kernel density estimate based on the MLE of the distribution function of the unobservable (uncorrupted) data.